If Father's age is 1 less than twice the son's age, what is

Question

If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son

Bunuel · Accepted Answer

Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37 .

Answer: A.

Hope it's clear.

KarishmaB · Answer

Look at the big picture. You can solve this question quickly using intuition.

Father's age is almost as much as twice of son's age. (just 1 less)
Son's age = NM, Father's age = MN

Say, son's age is 12 then father's is 21 (3 less than twice)
Say, son's age is 13 then father's is 31 (much more than twice)
I hope you understand that you can give up on the 10s series here because the gap will keep widening (diff b/w 14 and 41 will be even more)

Say, son's age is 24 then father's is 42 (much less than twice)
Say, son's age is 25, then father's is 52 (more than twice so give up on the 20s series too)

Say son's age is 36, then father's is 63 (much less than twice)
Say son's age is 37, then father's is 73 (1 less than twice. Got it!)

It's easy to say that there will be no other such combination because 49, 94 doesn't work. Nothing in 50s, 60s and so on will work because we need to stick to 2 digit numbers.

Hence, only statement 1 is sufficient.

docabuzar · Answer

Its all in the wording. Father is 1 less than twice of son, so in other words twice of son is 1 more than father

F = 2S -1

Had it been like " Father is 1 more than twice the son " then F=2S+1 or F-1=2S.

Hope I have added some thing.

subhajeet · Answer

Hey thanks for the explanation. I just messed up with the words.

Bunuel · Answer

It's all about word translation: father's age is 1 less than twice the son's age, so F is less than 2S by 1 --> so we need to add 1 to F to get 2S --> F+1=2S.

Hope it's clear

stampap · Answer

Hello can you elaborate if it is possible? how did we come up with F=10M+N and S=10N+M , Basically i understood how u solved it but i cannot comprehend the way we approach it initially

Thank you in advance

Bunuel · Answer

This is a way of writing a two-digit number. Any two-digit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc.

stampap · Answer

Oh yes! silly me , i had completely forgot it , now its clear!

thank you bunuel

minustark · Answer

1) 10M + N = 2(10N + M) -1 
10M + N =20N + 2M -1
8M = 19N -1 
19N - 8M = 1
N and M both can assume integer value between 1 to 9. So, the highest value 8M can take is 72. To make this statement true, N has to be 3 and M has to be 7 only. No other integer will make the statement true. SUFFICIENT.

2) Father's age can be any odd number greater or equal to 51 to make this statement true. Not sufficient.
A is the answer.

stepharr · Answer

Bunuel  in your statement #2, shouldn't "S" be "F" (Father), and "N" be "S" (Son)?

Bunuel · Answer

Yes, it should have been: (2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37.

Thank you. Edited.

Kinshook · Answer

Asked: If Father's age is 1 less than twice the son's age, what is the son's age?

Let f be father's age and s be son's age.
f = 2s - 1; s=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
f= 10M + N 
s = 10N + M
10M + N = 2(10N + M) - 1 = 20 N + 2M - 1
8M = 19N - 1
N = (8M + 1)/19
(M,N) = (7,3)
s = 37 = Son's age
SUFFICIENT

(2) Father is at least 25 years older than son
f >= s + 25
2s - 1 >= s + 25
s >=26
NOT SUFFICIENT

IMO A

Archit3110 · Answer

given
F = 2S-1
find S ; 
#1
The digits MN making up the father's age are reversed in the son's age i.e NM.
10a+b=10b+a
10a+b=20b+2a-1
8a=19b-1
8a+1=19b
for a = 7 and b = 3
so father is 73 and Son ; 37
sufficient
#2
Father is at least 25 years older than son
F=2s-1
26 = 2s
s= 13
least Son is 13 and Father = 25
son = 14 ; father = 27
many possibilities
insufficient
OPTION A

Dereno · Answer

Fathers age be F and sons age be S

F = 2S -1 —————— equation 1

Considering statement 2, which specifies a range band, which is not sufficient to attack.

Let’s look at statement 1, F = 10M + N

And son S = 10N + M

Substitute F and S in equation 1, we get

10M + N = 2( 10N + M ) -1

1 = 19 N - 8 M

we know the multiples of 8 = 8, 16, 24, 32, 40, 48,  56 , 64, 72.

19 multiples are = 19, 38,  57 .. yeah we have a number .

1 = 19 N - 8 M.  This becomes 19*3 - 8*7 = 1

fathers age F is 73 
and sons age is 37.

Hence  option A is SUFFICIENT

If Father's age is 1 less than twice the son's age, what is

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If Father's age is 1 less than twice the son's age, what is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards